{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import gym\n",
    "from gym import wrappers\n",
    "import gym_custom_envs\n",
    "import time as tt\n",
    "from gekko import GEKKO\n",
    "env = gym.make('Quadrotor2D-trajopt-v0', dt=0.01)\n",
    "# env = gym.wrappers.Monitor(env, \"vid\", force=True)\n",
    "m = GEKKO(remote=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "mass = env.m\n",
    "Inertia = env.I\n",
    "gravity = env.gravity\n",
    "r = env.l/2\n",
    "length = env.l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 3\n",
    "m.time = np.linspace(0,T,int(T/env.dt))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Control Force\n",
    "u1i = m.Var(value=mass*gravity, lb=-20*env.thrust_max, ub=20*env.thrust_max)\n",
    "u2i = m.Var(value=mass*gravity, lb=-20*env.thrust_max, ub=20*env.thrust_max)\n",
    "\n",
    "s = env.reset().reshape(6, 1)\n",
    "\n",
    "#State Variables\n",
    "xi = m.Var(value=s[0, 0], lb = -env.x_threshold, ub = env.x_threshold)\n",
    "yi = m.Var(value=s[1, 0], lb = -env.y_threshold, ub = env.y_threshold)\n",
    "thetai = m.Var(value=s[2, 0], lb = -env.O_threshold, ub = env.O_threshold)\n",
    "\n",
    "dxi = m.Var(value=s[3, 0])\n",
    "dyi = m.Var(value=s[4, 0])\n",
    "dthetai = m.Var(value=s[5, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<gekko.gekko.EquationObj at 0x7f0216819b80>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Defining the State Space Model\n",
    "m.Equation(xi.dt() == dxi)\n",
    "m.Equation(yi.dt() == dyi)\n",
    "m.Equation(thetai.dt() == dthetai)\n",
    "\n",
    "m.Equation(dxi.dt() == -((u1i + u2i)*m.sin(thetai)/mass))\n",
    "m.Equation(dyi.dt() == (((u1i + u2i)*m.cos(thetai) - (mass*gravity))/mass))\n",
    "m.Equation(dthetai.dt() == ((u1i - u2i)*r/Inertia))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Definine the Objectives\n",
    "# Make all the state variables be zero at time >= 2.2\n",
    "# m.Obj(xi**2)\n",
    "# m.Obj(yi**2)\n",
    "# m.Obj(thetai**2)\n",
    "m.fix(xi, pos=len(m.time) - 1, val=0)\n",
    "m.fix(yi, pos=len(m.time) - 1, val=0)\n",
    "m.fix(thetai, pos=len(m.time) - 1, val=0)\n",
    "m.fix(dxi, pos=len(m.time) - 1, val=0)\n",
    "m.fix(dyi, pos=len(m.time) - 1, val=0)\n",
    "m.fix(dthetai, pos=len(m.time) - 1, val=0)\n",
    "# m.Obj(dyi**2)\n",
    "# m.Obj(dxi**2)\n",
    "# m.Obj(dthetai**2)\n",
    "#Try to minimize change of MV over all horizon\n",
    "m.Obj(u1i**2)\n",
    "m.Obj(u2i**2)\n",
    "m.fix(u1i, pos=len(m.time) - 1, val=mass*gravity/2)\n",
    "m.fix(u2i, pos=len(m.time) - 1, val=mass*gravity/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "apm 106.206.74.222_gk_model0 <br><pre> ----------------------------------------------------------------\n",
      " APMonitor, Version 0.9.2\n",
      " APMonitor Optimization Suite\n",
      " ----------------------------------------------------------------\n",
      " \n",
      " \n",
      " --------- APM Model Size ------------\n",
      " Each time step contains\n",
      "   Objects      :            0\n",
      "   Constants    :            0\n",
      "   Variables    :            8\n",
      "   Intermediates:            0\n",
      "   Connections  :           16\n",
      "   Equations    :            8\n",
      "   Residuals    :            8\n",
      " \n",
      " Number of state variables:           4172\n",
      " Number of total equations: -         3588\n",
      " Number of slack variables: -            0\n",
      " ---------------------------------------\n",
      " Degrees of freedom       :            584\n",
      " \n",
      " **********************************************\n",
      " Dynamic Control with Interior Point Solver\n",
      " **********************************************\n",
      "  \n",
      "  \n",
      " Info: Exact Hessian\n",
      "\n",
      "******************************************************************************\n",
      "This program contains Ipopt, a library for large-scale nonlinear optimization.\n",
      " Ipopt is released as open source code under the Eclipse Public License (EPL).\n",
      "         For more information visit http://projects.coin-or.org/Ipopt\n",
      "******************************************************************************\n",
      "\n",
      "This is Ipopt version 3.12.10, running with linear solver ma57.\n",
      "\n",
      "Number of nonzeros in equality constraint Jacobian...:    10430\n",
      "Number of nonzeros in inequality constraint Jacobian.:        0\n",
      "Number of nonzeros in Lagrangian Hessian.............:     1490\n",
      "\n",
      "Total number of variables............................:     4172\n",
      "                     variables with only lower bounds:        0\n",
      "                variables with lower and upper bounds:     1490\n",
      "                     variables with only upper bounds:        0\n",
      "Total number of equality constraints.................:     3588\n",
      "Total number of inequality constraints...............:        0\n",
      "        inequality constraints with only lower bounds:        0\n",
      "   inequality constraints with lower and upper bounds:        0\n",
      "        inequality constraints with only upper bounds:        0\n",
      "\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "   0  2.3860000e+03 2.61e+01 8.00e+00   0.0 0.00e+00    -  0.00e+00 0.00e+00   0\n",
      "   1  4.5035191e+02 4.30e+01 9.99e+00   0.3 2.63e+02    -  9.86e-01 1.00e+00f  1\n",
      "   2  4.3751399e+02 2.28e+01 3.10e+01   0.1 2.22e+02    -  9.34e-01 1.00e+00h  1\n",
      "   3  6.7361723e+02 2.68e+01 1.44e+01  -0.2 1.83e+01  -2.0 9.45e-01 1.00e+00h  1\n",
      "   4  3.1184230e+02 2.62e+01 6.19e+00  -0.3 1.69e+01  -2.5 9.23e-01 9.86e-01f  1\n",
      "   5  7.6435199e+02 1.63e+01 3.01e+01  -6.3 1.99e+01  -3.0 7.48e-02 1.00e+00h  1\n",
      "   6  5.6764505e+02 8.00e+00 8.74e+00  -6.3 1.76e+01  -2.5 3.96e-01 1.00e+00f  1\n",
      "   7  6.6626090e+02 2.88e+00 7.92e+00  -6.6 3.93e+01    -  1.56e-01 1.00e+00h  1\n",
      "   8  6.6015355e+02 1.74e+00 2.31e+00  -0.6 5.73e+01    -  6.75e-01 1.00e+00f  1\n",
      "   9  6.5727713e+02 9.60e-02 2.12e-01  -1.6 3.70e+00  -3.0 9.99e-01 1.00e+00h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  10  6.5893526e+02 2.60e-01 1.33e+00  -2.6 3.54e+01    -  9.94e-01 1.00e+00H  1\n",
      "  11  6.5790106e+02 6.81e-02 6.88e-02  -4.2 7.77e+00    -  1.00e+00 1.00e+00h  1\n",
      "  12  6.5773112e+02 1.57e-03 1.27e-03  -5.7 6.44e-01  -3.5 1.00e+00 1.00e+00h  1\n",
      "  13  6.5771646e+02 3.71e-05 7.05e-03  -7.8 2.16e+00  -4.0 1.00e+00 1.00e+00H  1\n",
      "  14  6.5766059e+02 5.28e-03 8.81e-02  -9.6 8.20e+00  -4.4 1.00e+00 1.00e+00H  1\n",
      "  15  6.4216253e+02 4.20e+00 5.75e-01 -10.6 4.97e+01  -4.9 1.00e+00 1.00e+00H  1\n",
      "  16  6.6149304e+02 1.20e+00 7.50e-01 -11.0 2.33e+01    -  1.00e+00 1.00e+00h  1\n",
      "  17  6.6159254e+02 1.19e+00 7.46e-01 -11.0 2.47e+01    -  1.00e+00 1.00e+00h  1\n",
      "  18  6.6010924e+02 8.96e-01 5.94e-01 -11.0 2.12e+01    -  1.00e+00 1.00e+00f  1\n",
      "  19  6.5643031e+02 6.51e-02 6.40e-01 -11.0 2.26e+01    -  1.00e+00 1.00e+00H  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  20  6.5641441e+02 1.73e-02 3.98e-01 -11.0 1.72e+01    -  1.00e+00 1.00e+00H  1\n",
      "  21  6.5603750e+02 8.96e-02 6.02e-01 -11.0 2.22e+01    -  1.00e+00 1.00e+00H  1\n",
      "  22  6.5621131e+02 3.66e-03 2.22e-01 -11.0 1.27e+01    -  1.00e+00 1.00e+00H  1\n",
      "  23  6.5527282e+02 2.60e-01 8.11e-01 -11.0 2.61e+01    -  1.00e+00 1.00e+00H  1\n",
      "  24  6.5642408e+02 1.14e-01 9.24e-02 -11.0 8.35e+00    -  1.00e+00 1.00e+00h  1\n",
      "  25  6.4931224e+02 1.97e+00 1.09e+00 -11.0 4.08e+01    -  1.00e+00 1.00e+00H  1\n",
      "  26  6.5604456e+02 5.04e-02 4.44e-02 -11.0 6.26e+00    -  1.00e+00 1.00e+00h  1\n",
      "  27  6.3445715e+02 6.25e+00 1.50e-01 -11.0 5.57e+01    -  1.00e+00 1.00e+00H  1\n",
      "  28  6.5850175e+02 8.28e-01 5.47e-01 -11.0 1.81e+01    -  1.00e+00 1.00e+00h  1\n",
      "  29  6.5612891e+02 7.17e-02 5.37e-02 -11.0 6.68e+00    -  1.00e+00 1.00e+00h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  30  6.4888626e+02 1.99e+00 5.52e-01 -11.0 3.60e+01    -  1.00e+00 1.00e+00H  1\n",
      "  31  6.5590383e+02 3.10e-02 2.55e-02 -11.0 4.23e+00    -  1.00e+00 1.00e+00h  1\n",
      "  32  6.3738433e+02 5.29e+00 1.91e-02 -11.0 5.00e+01    -  1.00e+00 1.00e+00H  1\n",
      "  33  6.5948268e+02 9.28e-01 2.61e+00 -11.0 7.85e+01    -  1.00e+00 5.00e-01h  2\n",
      "  34  6.5586627e+02 6.24e-02 7.42e-02 -11.0 1.02e+01    -  1.00e+00 1.00e+00h  1\n",
      "  35  6.5544925e+02 9.12e-02 2.02e-01 -11.0 1.36e+01    -  1.00e+00 1.00e+00H  1\n",
      "  36  6.5590754e+02 3.86e-02 2.79e-02 -11.0 4.33e+00    -  1.00e+00 1.00e+00h  1\n",
      "  37  6.5322032e+02 7.07e-01 2.58e-01 -11.0 2.23e+01    -  1.00e+00 1.00e+00H  1\n",
      "  38  6.5580843e+02 1.51e-02 1.22e-02 -11.0 2.85e+00    -  1.00e+00 1.00e+00h  1\n",
      "  39  6.4867196e+02 1.97e+00 1.36e-02 -11.0 2.99e+01    -  1.00e+00 1.00e+00H  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  40  6.6054003e+02 1.31e+00 9.02e-01 -11.0 2.39e+01    -  1.00e+00 1.00e+00h  1\n",
      "  41  6.5577136e+02 1.22e-02 1.31e-02 -11.0 4.37e+00    -  1.00e+00 1.00e+00h  1\n",
      "  42  6.5498697e+02 2.09e-01 1.01e-01 -11.0 1.28e+01    -  1.00e+00 1.00e+00H  1\n",
      "  43  6.5577317e+02 7.59e-03 5.64e-03 -11.0 1.91e+00    -  1.00e+00 1.00e+00h  1\n",
      "  44  6.5490185e+02 2.31e-01 5.70e-02 -11.0 1.19e+01    -  1.00e+00 1.00e+00H  1\n",
      "  45  6.5576854e+02 6.39e-03 4.38e-03 -11.0 1.70e+00    -  1.00e+00 1.00e+00h  1\n",
      "  46  6.5556842e+02 4.84e-02 3.32e-02 -11.0 6.71e+00    -  1.00e+00 1.00e+00H  1\n",
      "  47  6.5575425e+02 2.47e-03 1.72e-03 -11.0 1.06e+00    -  1.00e+00 1.00e+00h  1\n",
      "  48  6.5572554e+02 5.40e-03 8.83e-03 -11.0 2.96e+00    -  1.00e+00 1.00e+00H  1\n",
      "  49  6.5574707e+02 4.97e-04 3.30e-04 -11.0 4.70e-01    -  1.00e+00 1.00e+00h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  50  6.5574662e+02 3.72e-04 2.27e-04 -11.0 4.04e-01    -  1.00e+00 1.00e+00h  1\n",
      "  51  6.5574526e+02 3.38e-07 2.26e-07 -11.0 1.23e-02    -  1.00e+00 1.00e+00h  1\n",
      "\n",
      "Number of Iterations....: 51\n",
      "\n",
      "                                   (scaled)                 (unscaled)\n",
      "Objective...............:   6.5574526031145285e+02    6.5574526031145285e+02\n",
      "Dual infeasibility......:   2.2626527193345741e-07    2.2626527193345741e-07\n",
      "Constraint violation....:   3.3844871083488215e-07    3.3844871083488215e-07\n",
      "Complementarity.........:   1.0000000000000003e-11    1.0000000000000003e-11\n",
      "Overall NLP error.......:   3.3844871083488215e-07    3.3844871083488215e-07\n",
      "\n",
      "\n",
      "Number of objective function evaluations             = 74\n",
      "Number of objective gradient evaluations             = 52\n",
      "Number of equality constraint evaluations            = 74\n",
      "Number of inequality constraint evaluations          = 0\n",
      "Number of equality constraint Jacobian evaluations   = 52\n",
      "Number of inequality constraint Jacobian evaluations = 0\n",
      "Number of Lagrangian Hessian evaluations             = 51\n",
      "Total CPU secs in IPOPT (w/o function evaluations)   =      0.519\n",
      "Total CPU secs in NLP function evaluations           =      1.706\n",
      "\n",
      "EXIT: Optimal Solution Found.\n",
      " \n",
      " The solution was found.\n",
      " \n",
      " The final value of the objective function is    655.745260311453     \n",
      " \n",
      " ---------------------------------------------------\n",
      " Solver         :  IPOPT (v3.12)\n",
      " Solution time  :    2.26919999999882      sec\n",
      " Objective      :    655.745260311453     \n",
      " Successful solution\n",
      " ---------------------------------------------------\n",
      " \n"
     ]
    }
   ],
   "source": [
    "m.options.IMODE = 6 # MPC\n",
    "# m.options.SOLVER = 3\n",
    "m.solve() #(disp=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(0.0, 3.0)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.subplot(311)\n",
    "plt.plot(m.time,u2i.value,'m', m.time, u1i.value,'c')\n",
    "plt.legend([r'$u1, u2$'],loc=1)\n",
    "plt.ylabel('Force')\n",
    "plt.xlabel('Time')\n",
    "plt.xlim(m.time[0],m.time[-1])\n",
    "\n",
    "plt.subplot(312)\n",
    "plt.plot(m.time,dxi.value,'r', m.time, dyi.value,'g', m.time,dthetai.value,'b')\n",
    "plt.legend([r'$x_{dot}, y_{dot}, theta_{dot}]$'],loc=1)\n",
    "plt.ylabel('Velocity')\n",
    "plt.xlabel('Time')\n",
    "plt.xlim(m.time[0],m.time[-1])\n",
    "\n",
    "plt.subplot(313)\n",
    "plt.plot(m.time,xi.value,'r', m.time, yi.value,'g', m.time,thetai.value,'b',)\n",
    "plt.legend([r'$x, y, theta$'],loc=1)\n",
    "plt.ylabel('Position')\n",
    "plt.xlabel('Time')\n",
    "plt.xlim(m.time[0],m.time[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "done = False\n",
    "j = 0\n",
    "while not done:\n",
    "    a = [xi.value[j], yi.value[j], thetai.value[j], \n",
    "         dxi.value[j], dyi.value[j], dthetai.value[j],\n",
    "         u1i.value[j], u2i.value[j]]\n",
    "    ns, c, done,_ = env.step(a)\n",
    "    s = ns.reshape(6, 1)\n",
    "    env.render()\n",
    "    j += 1\n",
    "env.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
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 "nbformat": 4,
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